Question

Let f : R – (- \(\frac { 4 }{ 3 }\)) → R be a function, defined as f(x) = \(\frac { 4x }{ 3x+4 }\), x ≠ – \(\frac { 4 }{ 5 }\).

The inverse off is map g: Range f → R – is given by \(\frac { 4 }{ 3 }\) is given by

(A) g(y) = \(\frac { 3y }{ 3-4y }\)

(B) g(y) = \(\frac { 4y }{ 4-3y }\)

(C) g(y) = \(\frac { 4y }{ 3-4y }\)

(D) g(y) = \(\frac { 3y }{ 4-3y }\)

Answer 1

f : R – {\(\frac { -4 }{ 3 }\)} → R is a function defined by f(x) = \(\frac { 4x }{ 3x+4 }\)

Let y = \(\frac { 4x }{ 3x+4 }\).

⇒ 3xy + 4y = 4x

or x(4 – 3y) = 4y

∴ x = \(\frac { 4y }{ 4-3y }\)

∴ f-1(4y) = g(y) = \(\frac { 4y }{ 4-3y }\)

So, part (B) is the correct answer.